Solving the graph coloring problem using cuckoo search

Abstract

We adapt the Cuckoo Search (CS) algorithm for solving the three color Graph Coloring Problem (3-GCP). The difficulty of this task is adapting CS from a continuous to a discrete domain. Previous researches used sigmoid functions to discretize the Lévi Flight (LF) operator characteristic of CS, but this approach does not take into account the concept of Solution Distance, one of the main characteristics of LF. In this paper, we propose a new discretization of CS that maintains LF’s solution distance concept. We also simplify CS’s parasitism operator, reducing the number of evaluations necessary. We compare different combinations of the proposed changes, using GA as a baseline, on a set of randomly generated 3-GCP problems. The results show the importance of a good discretization of the LF operator to increase the success rate and provide auto-adaptation to the CS algorithm.